Papers by Wilfried Schmid
Bookmarks Related papers MentionsView impact
Non-Commutative Harmonic Analysis, 1975
Page 1. SOME REMARKS ABOUT THE DISCRETE SERIES CHARACTERS OF Sp(n,R)Wilfried Schmid* Let G be a c... more Page 1. SOME REMARKS ABOUT THE DISCRETE SERIES CHARACTERS OF Sp(n,R)Wilfried Schmid* Let G be a connected, semisimple Lie group, whlch admits a faithful finite-dimensional representation, and let K be a maximal compact subgroup. ...
Bookmarks Related papers MentionsView impact
In these notes, I shall describe two character formulas for semisimple Lie groups. Both are of in... more In these notes, I shall describe two character formulas for semisimple Lie groups. Both are of interest by themselves, but the potential connections between the two formulas raise some intriguing questions. The formulas represent joint work with Kari Vilonen; full details will appear elsewhere. The formulas and their relation are well understood in the case of a compact group. For motivation, I shall start out with a discussion of the compact case. Thus I consider K, a connected, compact Lie group, and T ⊂ K, a maximal torus. I write kR, tR for the Lie algebras of K, T , and k, t for their complexified Lie algebras. Let π be an irreducible unitary representation of K. Because of the compactness of K, π must be finite dimensional. The Weyl character formula describes the character Θπ as a function of T , and thus – since the maximal torus meets every conjugacy class – globally as function on all of K. To recall the formula, I use the exponential map to identify the torus T with the q...
Bookmarks Related papers MentionsView impact
Lie Theory and Geometry, 1994
Bookmarks Related papers MentionsView impact
Progress in Mathematics
An accessory mountable on a toilet, so as to prevent males, during urination, from urinating on a... more An accessory mountable on a toilet, so as to prevent males, during urination, from urinating on a floor or on the toilet; the accessory including a cylindrical shaped shield made of plastic or rubber, and which is accordion pleated, so as to collapse and fold underneath the toilet seat, the shield being upwardly extendable by means of operation of a foot pedal, and which in its upward extended position shields against urine splashing outwardly from the toilet.
Bookmarks Related papers MentionsView impact
Journal of the American Mathematical Society, 1998
In this paper we prove two formulas for the characters of representations of reductive groups. Bo... more In this paper we prove two formulas for the characters of representations of reductive groups. Both express the character of a representation π \pi in terms of the same geometric data attached to π \pi . When specialized to the case of a compact Lie group, one of them reduces to Kirillov’s character formula in the compact case, and the other, to an application of the Atiyah-Bott fixed point formula to the Borel-Weil realization of the representation π \pi .
Bookmarks Related papers MentionsView impact
Proceedings of the American Mathematical Society, 1984
Bookmarks Related papers MentionsView impact
Contemporary Mathematics, 2016
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Progress in mathematics, 1991
Typically, irreducible Harish-Chandra modules are constructed not directly, but as unique irreduc... more Typically, irreducible Harish-Chandra modules are constructed not directly, but as unique irreducible submodules, or unique irreducible quotients, of so-called standard modules. As in some other contexts, standard modules are obtained by cohomological constructions which tend to be “easy” on the level of Euler characteristic. For certain values of the parameters in these constructions, there is a vanishing theorem; standard modules arise when the vanishing theorem applies.
Bookmarks Related papers MentionsView impact
Lecture Notes in Mathematics, Nov 14, 2006
Bookmarks Related papers MentionsView impact
Lecture Notes in Mathematics, 1974
Page 1. Abbildungen in arithmetische Quotienten hermitesch symmetrischer R~ume WilfriedSchmid ) I... more Page 1. Abbildungen in arithmetische Quotienten hermitesch symmetrischer R~ume WilfriedSchmid ) In den Arbeiten [4,5, ~ ~ hat Phillip Griffiths den Versuch begonnen, die klassische Theorie der Moduln Riemannscher FiMchen fHr beliebige ...
Bookmarks Related papers MentionsView impact
Thomas B Fordham Foundation and Institute, 2005
Bookmarks Related papers MentionsView impact
Contemporary Mathematics, 2011
Bookmarks Related papers MentionsView impact
Let \( \Delta = \{ z \in \mathbb{C}:|z| < 1\} ,\;{{S}^{1}} = \partial \Delta \). For u in C(S ... more Let \( \Delta = \{ z \in \mathbb{C}:|z| < 1\} ,\;{{S}^{1}} = \partial \Delta \). For u in C(S 1), let Pu denote the Poisson transform of u: $$ {{P}_{u}}\left( {r{{e}^{{i\theta }}}} \right) = \frac{1}{{2\pi }}\int_{0}^{{2\pi }} {\frac{{1 - {{r}^{2}}}}{{1 + {{r}^{2}} - 2r\cos (\theta - \varphi )}}u({{e}^{{i\varphi }}})d\varphi .} \; $$ (a)
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Representations of Lie Groups, Kyoto, Hiroshima, 1986, 1988
Publisher Summary This chapter describes the geometric constructions of representations. There is... more Publisher Summary This chapter describes the geometric constructions of representations. There is a close connection between representations of a Lie group G and its coadjoint orbits, that is, G -orbits in the dual of the Lie algebra. In the case of a nilpotent group, unitary representations correspond to coadjoint orbits equipped with real polarizations, and the correspondence has been used by Kirillov to construct the representations. Harish-Chandra's parametrization of those unitary representations that enter the Plancherel decomposition of L 2 (G) , with G semisimple, are phrased in terms of coadjoint orbits, though his construction ties the representations only indirectly to the orbits in question. The chapter describes recent results on the orbit method for semisimple coadjoint orbits of semisimple Lie groups, without restriction on the type of polarization.
Bookmarks Related papers MentionsView impact
Progress in Mathematics
Bookmarks Related papers MentionsView impact
Harmonic Analysis and Representations of Semisimple Lie Groups, 1980
In the above paper [2] a key role is played by a result of Borel [3], concerning discrete subgrou... more In the above paper [2] a key role is played by a result of Borel [3], concerning discrete subgroups Г of semisimple Lie groups G. They prove that if G is linear, one can find a torsion-free Г with Г\G compact. Unfortunately we applied this result in [2] even for non-linear G, in which case the existence of such Г is seriously in doubt, as pointed out to us by P. Deligne and J. P. Serre. The difficulty is that a torsion-free subgroup of the adjoint group lifts to a cocompact subgroup Г ⊂ G which contains the (finite) center Z of G, and there may be an obstruction to removing this torsion subgroup. As it stands, [2] is correct only for linear G, and we shall now indicate how to extend the proof to cover all G.
Bookmarks Related papers MentionsView impact
Contemporary Mathematics, 2008
Bookmarks Related papers MentionsView impact
Uploads
Papers by Wilfried Schmid